The Marseille Hospital Authority said Sunday that Jarreau is getting better and in good spirits but will stay in La Timone hospital for monitoring.
Jarreau's managers says he will undergo tests in Marseille and "hopes to resume his tour at the end of the coming week."
The 70-year-old Jarreau was hospitalized in the Alps on Friday after suffering breathing problems in the mountains that forced him to cancel several concerts. He was moved to Marseille by helicopter Saturday.
Jarreau has won Grammys in three separate categories - jazz, pop and R&B.